brief, short
blow-by-blow (informal), comprehensive, detailed, full, graphic
He gave us a blow-by-blow account of the incident.

fascinating, vivid
accurate, clear, factual, true
eyewitness, first-hand, personal
glowing, good
She received a glowing account of her son's progress.

media, news (AmE), newspaper
the newspaper account of the trial

fictional, fictionalized
autobiographical
historical
biblical

give (sb), offer, provide (sb with), write (sb)
Can you give us an account of what happened?

publish

in an/the account
Dr Richards describes this very well in his account of the events.

by all accounts (= according to what people say)
I've never been there, but it's a beautiful place by all accounts.

by sb's own account
By his own account he had an unhappy childhood.

bank, building-society (BrE)
checking (AmE), cheque (BrE), current
deposit (BrE), investment, savings
personal
business
individual, joint, separate
My husband and I have separate accounts.

numbered, private (esp. AmE)
They have a numbered account in Switzerland.

high-interest, interest-bearing, tax-free
offshore
brokerage (esp. AmE), money-market, trust
retirement (esp. AmE)

have, hold
Go and see the manager of the bank where your account is held.

close, open
She opened a savings account at the bank.

credit sth to, pay sth into (esp. BrE), put sth into
The money will be credited to your account tomorrow.

debit (sth from), draw sth out of, pay sth from, take sth out of, withdraw sth from
She had taken all her money out of her account.

access
empty, overdraw
Your account is overdrawn.

number
holder
balance

account at
He opened an account at a bank in Germany.

account with
I have an account with another bank.

profit and loss account
accounts payable, accounts receivable

do, keep
Try to keep accurate accounts.

audit, check, look at
submit
Your accounts will need to be submitted to the tax office.

publish

be in order
The accounts are all in order.

account book
account balance

expense (= an arrangement to charge expenses to your own employers)
Clients are often taken for expense account lunches.

charge (= an arrangement with a shop/store to pay bills for goods or services at a later time), credit (BrE)
email, user

have
create, open
I'd like to open an account, please.

close
pay off, settle
It is best to settle the account each month.

charge sth to, debit (sth from), put sth on
Charge this to my account, please.

credit sth to

on account
Call a cab on account.

account at, account with
an account with a large store